It is becoming apparent that in the future battery systems will increasingly be used both in stationary applications and in vehicles such as hybrid and electric vehicles. In order to be able to fulfill the requirements provided for a respective application in respect of voltage and available power, a high number of battery cells are connected in series. Owing to the series connection, the failure of one battery cell can lead to the failure of the battery and this in turn can lead to a failure of the overall system, for which reason, in particular for safety-relevant applications, stringent requirements are made of the reliability of the battery. In order to be able to detect the state of the battery and of the individual battery cells as accurately as possible and thus identify an imminent failure of a battery cell in good time, alongside other parameters of the battery or battery cells in particular the voltages, too, of the battery cells are measured regularly. The prior art discloses numerous methods which carry out so-called cell balancing, that is to say seek to match the charge states of the different battery cells of a battery to one another, which has a positive effect on the lifetime of the battery. For this purpose, the battery is equipped with units which determine the cell voltages of the individual battery cells and optionally further measurement variables such as battery temperature and battery current and communicate them to a central control unit (for example a microcontroller). The control unit calculates a respective charge state from the communicated measurement data for each battery cell and generates the control signals necessary for carrying out cell balancing, which control signals bring about the charge equalization among the battery cells in the battery by, for example, battery cells that have a higher charge state being partly discharged. In this case, the control unit is arranged outside the battery in order to be able to perform further tasks. However, this entails the disadvantage that relatively complex safety measures such as isolators arranged in the data path have to be implemented in order to prevent, in the case of a fault, a short circuit between the high battery voltage (often hundreds of volts in the case of battery-operated drive systems) and the parts which are arranged in the low-voltage power supply system and can be touched externally, such as the control unit.